Explanation

(a) $W = \ \frac{F^{2}l}{2\left( \frac{\pi D^{2}}{4} \right)Y}$
$Y,\ l\ and\ F$ are constants.
$\therefore\ W\ \propto \frac{1}{D^{2}}$
$\therefore\ \ \frac{W_{1}}{W_{2}} = \frac{D_{2}^{2}}{D_{1}^{2}} = 16$ …….(i)
Now , $W_{1} = \frac{1}{2} \times 10^{3} \times 1 \times 10^{- 3} = 0.5\ J$
$W_{2} = \frac{1}{2} \times 10^{3} \times \frac{10^{- 3}}{16} = \frac{1}{32} = 0.03125$
Again , $\frac{W_{1}}{W_{2}} = \frac{0.5}{0.03125} = 16$ ………..(ii)
Answer is confirmed by comparing Eqs. (i) and (ii) .